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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<a NAME="E1:16"/>
( ( <font color="Maroon">p</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">q</font> implies <span class="p1"><a href="filter_1.html#K9">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font></span><a href="filter_1.html#K9">]</a></span> <a href="hidden.html#R2">in</a>  <a href="lattice3.html#K2" target="_self">LattRel</a> <font color="Maroon">L</font> ) &amp; ( <span class="p1"><a href="filter_1.html#K9">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font></span><a href="filter_1.html#K9">]</a></span> <a href="hidden.html#R2">in</a>  <a href="lattice3.html#K2" target="_self">LattRel</a> <font color="Maroon">L</font> implies <font color="Maroon">p</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">q</font> ) &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="lattice3.html#K4" target="_self">%</a>  &amp; <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="lattice3.html#K4" target="_self">%</a>  &amp;  <a href="lattice3.html#K3" target="_self">LattPOSet</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font>),<span class="p1">(<span class="default"><a href="lattice3.html#K2" target="_self">LattRel</a> <font color="Maroon">L</font></span>)</span> #) )
 
<b>by </b><i><a class="ref" href="filter_1.html#T32">FILTER_1:32</a></i>;<br/>
<b>hence </b><a NAME="E2:16"/>
( <font color="Maroon">p</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">q</font> iff <font color="Maroon">p</font> <a href="lattice3.html#K4" target="_self">%</a>  <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">q</font> <a href="lattice3.html#K4" target="_self">%</a>  )
 <b>by </b><i><a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a></i>;<br/>


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